{"id":"cb_question_bank:95fe0b37-8049-4d0c-9e92-4b9643d2f206","source_id":"cb_question_bank","source_item_id":"95fe0b37-8049-4d0c-9e92-4b9643d2f206","external_id":"55751ff1-1079-45a7-b117-348b4d276815","ibn":null,"question_id":"ffb371f5","program":"SAT","module":"math","domain_code":"H","domain":"Algebra","skill_code":"H.D.","skill":"Systems of two linear equations in two variables","difficulty":"E","score_band":2,"answer_type":"mcq","answer_source":"key","layout_warning":null,"form_id":null,"module_number":null,"position":null,"stem":"3 x equals 12 negative 3 x plus y equals negative 6 The solution to the given system of equations is left parenthesis x comma y right parenthesis . What is the value of y ?","stimulus":"","stimulus_html":null,"stem_html":"<p style=\"text-align: center;\"><math alttext=\"3 x equals 12\"><mrow><mn>3</mn></mrow><mi>x</mi><mo>=</mo><mrow><mn>12</mn></mrow></math></p>\n<p style=\"text-align: center;\"><math alttext=\"negative 3 x plus y equals negative 6\"><mrow><mo>-</mo><mn>3</mn></mrow><mi>x</mi><mo>+</mo><mi>y</mi><mo>=</mo><mrow><mo>-</mo><mn>6</mn></mrow></math></p>\n<p style=\"text-align: left;\">The solution to the given system of equations is&nbsp;<math alttext=\"left parenthesis x comma y right parenthesis\"><mfenced><mrow><mi>x</mi><mo>,</mo><mi>y</mi></mrow></mfenced></math>. What is the value of <math alttext=\"y\"><mi>y</mi>\n</math>?</p>","rationale_html":"<p>Choice B is correct. Adding the second equation in the given system to the first equation in the given system yields <math alttext=\"3 x plus left parenthesis minus 3 x plus y right parenthesis equals 12 plus left parenthesis negative 6 right parenthesis\"><mn>3</mn><mi>x</mi><mo>+</mo><mo>(</mo><mo>-</mo><mn>3</mn><mi>x</mi><mo>+</mo><mi>y</mi><mo>)</mo><mo>=</mo><mn>12</mn><mo>+</mo><mfenced><mrow><mo>-</mo><mn>6</mn></mrow></mfenced></math>, which is equivalent to <math alttext=\"y equals 6\"><mi>y</mi><mo>=</mo><mn>6</mn></math>.&nbsp;</p>\n<p>Choice A is incorrect and may result from conceptual or calculation errors.</p>\n<p>Choice C is incorrect and may result from conceptual or calculation errors.</p>\n<p>Choice D is incorrect and may result from conceptual or calculation errors.</p>","correct_answer":["B"],"has_media":false,"has_mathml":true,"has_table":false,"source_created_at":"2023-08-02T20:25:59.817000+00:00","source_updated_at":"2023-08-02T20:25:59.817000+00:00","options":[{"label":"A","content_html":"<p><math alttext=\"negative 3\"><mo>-</mo><mn>3</mn>\n</math></p>","ord":0},{"label":"B","content_html":"<p><math alttext=\"6\"><mn>6</mn>\n</math></p>","ord":1},{"label":"C","content_html":"<p><math alttext=\"18\"><mn>18</mn>\n</math></p>","ord":2},{"label":"D","content_html":"<p><math alttext=\"30\"><mn>30</mn>\n</math></p>","ord":3}],"attribution":{"source_id":"cb_question_bank","source_name":"College Board digital SAT question bank (community dump)","rights_holder":"College Board","canonical_url":"https://satsuitequestionbank.collegeboard.org/","retrieved_from":"https://raw.githubusercontent.com/mdn522/sat-question-bank/main/data/cb-digital-questions.json","attribution":"SAT practice questions © College Board, from the official SAT Suite Question Bank. Retrieved via the community dump at github.com/mdn522/sat-question-bank.","disclaimer":"SAT® and PSAT/NMSQT® are trademarks registered by the College Board, which is not affiliated with, does not sponsor, and does not endorse this project.","license":"College Board copyright; source repository carries no licence. Local use only.","redistributable":false,"item_count":2017}}